Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
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Answer:
The order of operations is PEMDAS
First step is to do everything is parenthesis or brackets
5+{2*[(5-1)+6]}/4
{2*[(5-1)+6]}
First you would go 5-1=4, because that is the first equation that is in parenthesis by itself.
{2*[4+6]}
Next you would go 4+6=10, because that is your next smallest bracket
{2*10}
Last you would go 2*10=20
Your equation now looks like this
5+{20}/4
In PEMDAS your next step is exponents, but we don't have any so we go on to the next one which is multiply/division
5+5
You would go 20/4=5
Last step is to add/subtract
5+5=10
Your final answer would be 10
Hope this helps ;)
Step-by-step explanation:
Answer:
x^4+4x^3+8x^2+8x-5
Step-by-step explanation:
The relative change is 2%.
<h3>What is relative change?</h3>
In contrast to the reference value, the absolute change's size is expressed as a fraction called the relative change: relative change = absolute change reference value = new value reference value reference value. The absolute change is expressed as a percentage of the value of the indicator in the prior period, or "relative change" expresses the absolute change as such. When measuring indicators in percentage terms, such as the unemployment rate, absolute and relative change principles also apply. To determine the absolute change, subtract the starting value from the ending value. Simply deduct 1,000 from 1,100 to arrive at 100 in the example. The student population increased by 100 pupils throughout the course of the year because this is the absolute change.
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Answer:
the first and last one
Step-by-step explanation:
